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Mathematics - Properties of Triangles

Practise 31 JEE Main previous year questions on Properties of Triangles, compiled from papers spanning 2002 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty JEE Main tests.

Properties of Triangles has been asked in 15 of the 25 years of JEE Main papers analysed (2002–2026), with 31 questions in all. 3% of them were easy, 42% moderate and 55% tough. Most of its questions came from 2021, with 4 questions that year. In the last three years (2024–2026) it had 1 question across 49 papers, about 0 per paper.

The chapter's 5 topics are not weighted equally: Sine Rule and its application (12 questions, 39%), Circle and Polygon (10 questions, 32%), and Cosine Rule and Projection Formula (5 questions, 16%) have been asked the most. Over the last five years the most frequent topics have been Circle Connected to Triangle (1), Cosine Rule and Projection Formula (1), and Napiers Analogy, Area of Triangle & Half angle Formulae (1). Sine Rule and its application has produced the most tough questions (6).

  1. 1In a triangle and . If , where , then is equal to________06 Apr, 2024 (E)Cosine Rule and Projection Formula
  2. 2For a triangle A B C , the value of cos 2 A + cos 2 B + cos 2 C is least. If its inradius is 3 and incentre is M , then which of the followi01 Feb, 2023 (M)Circle Connected to Triangle
  3. 3Let a , b and c be the length of sides of a triangle A B C such that a + b 7 = b + c 8 = c + a 9 . If r and R are the radius of incircle and25 Jun, 2022 (M)Napiers Analogy, Area of Triangle & Half angle Formulae
  4. 4Let sin A sin B = sin ( A - C ) sin ( C - B ) , where A , B , C are angles of a triangle A B C . If the lengths of the sides opposite these 27 Aug, 2021 (M)Sine Rule and its application
  5. 5If in a triangle A B C , A B = 5 units, B = cos - 1 3 5 and radius of circumcircle of A B C is 5 units, then the area (in sq. units) of A B 20 Jul, 2021 (M)Sine Rule and its application
  6. 6Let in a right angled triangle, the smallest angle be . If a triangle formed by taking the reciprocal of its sides is also a right angled tr20 Jul, 2021 (E)Sine Rule and its application
  7. 7In ABC , the lengths of sides A C and A B are 12 cm and 5 cm , respectively. If the area of ABC is 30 cm 2 and R and r are respectively the 16 Mar, 2021 (E)Sine Rule and its application
  8. 8The angles A , B C of a A B C are in A . P . and a : b = 1 : 3 . If c = 4 c m , then the area (in s q . c m ) of this triangle is:10 Apr, 2019 (E)Sine Rule and its application
  9. 9If the lengths of the sides of a triangle are in A.P and the greatest angle is double the smallest, then a ratio of lengths of the sides of 08 Apr, 2019 (E)Sine Rule and its application
  10. 10Given for a with usual notation. If then the ordered triad has a value11 Jan, 2019 (E)Cosine Rule and Projection Formula
  11. 11With the usual notation in A B C , if A + B = 120 , a = 3 + 1 units and b = 3 - 1 units, then the ratio A : B is10 Jan, 2019 (E)Sine Rule and its application
  12. 12In a triangle A B C , coordinates of A are 1 , 2 and the equations of the medians through B and C are respectively, x + y = 5 and x = 4 . Th15 Apr, 2018Sine Rule and its application
  13. 13Let the orthocentre and centroid of a triangle be A - 3 , 5 and B 3 , 3 respectively. If C is the circumcentre of this triangle, then the ra08 Apr, 2018Sine Rule and its application
  14. 14Let and be the vertices of a . If the median through is equally inclined to the coordinate axes, then:11 Apr, 2014 (Online)Circle and Polygon
  15. 15If the extremities of the base of an isosceles triangle are the points and and the equation of one of the sides is , then the area of the tr23 Apr, 2013 (Online)Circle and Polygon
  16. 16On the sides of a distinct points (excluding vertices ) are respectively chosen. The number of triangles that can be constructed using these23 Apr, 2013 (Online)Circle and Polygon
  17. 17If two vertices of an equilateral triangle are and , and the third vertex C lies above -axis then the equation of the circumcircle of is :22 Apr, 2013 (Online)Napiers Analogy, Area of Triangle & Half angle Formulae
  18. 18If three distinct points are given in the 2dimensional coordinate plane such that the ratio of the distance of each one of them from the poi19 May, 2012 (Online)Circle and Polygon
  19. 19If in a triangle , then is equal to12 May, 2012 (Online)Cosine Rule and Projection Formula
  20. 20In a , if and , then the angle is equal to2012 (Offline)Sine Rule and its application
  21. 21For a regular polygon, let and be the radii of the inscribed and the circumscribed circles. A false statement among the following is2010Circle and Polygon
  22. 22A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same2006Circle and Polygon
  23. 23ABC is a triangle. Forces acting along and respectively are in equilibrium, where is the incentre of . Then is2005Circle and Polygon
  24. 24In a triangle . If and are the roots of then2005Circle and Polygon
  25. 25In a triangle , let . If is the inradius and is the circumradius of the the triangle , then equals2005Sine Rule and its application
  26. 26The sides of a triangle are and for some . Then the greatest angle of the triangle is2004Circle and Polygon
  27. 27The sum of the radii of inscribed and circumscribed circles for an sided regular polygon of side a, is2003Circle and Polygon
  28. 28In a triangle , medians and are drawn. If and , then the area of the is2003Sine Rule and its application
  29. 29If in a triangle , then the sides and2003Cosine Rule and Projection Formula
  30. 30The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is2002Circle Connected to Triangle
  31. 31In a triangle with sides (which are the ex-radii) then2002Cosine Rule and Projection Formula

Frequently Asked Questions

1.How many questions are available for Properties of Triangles?

This chapter includes 31 questions compiled from JEE Main papers spanning 2002 to 2024.

2.Are these questions only from JEE Main, or from other exams too?

These are JEE Main questions specifically for the Properties of Triangles chapter. Questions from other exams like NTA Abhyas (JEE Main) or JEE Advanced are organised separately under their respective exam sections.

3.Is Properties of Triangles an important chapter for JEE Main Mathematics?

Properties of Triangles has appeared in 15 of the 25 years of JEE Main papers covered here, with 31 questions across 25 papers - about one per paper it appears in.

4.What is the difficulty level of Properties of Triangles questions in JEE Main?

Of the 31 questions analysed for this chapter, 3% are easy, 42% moderate and 55% tough. 2021 had the most, with 4 questions.

5.Which topics in Properties of Triangles should I focus on?

These topics have carried the most weightage in Properties of Triangles:

  • Sine Rule and its application - 12 questions (39%)
  • Circle and Polygon - 10 questions (32%)
  • Cosine Rule and Projection Formula - 5 questions (16%)
  • Sine Rule and its application has produced the most tough questions (6).
6.Is Properties of Triangles's weightage in JEE Main going up or down?

Across all 25 papers analysed, Properties of Triangles has averaged about 1.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.